Kane's double in the 3-0 win at White Hart Lane means the Tottenham striker has now equalled last season's tally while his total haul in the top flight now stands at 45.
He also becomes only the fifth Englishman to hit 20 goals in consecutive Premier League campaigns, joining an esteemed group that includes Shearer, Les Ferdinand, Andy Cole and Robbie Fowler.
Shearer remains top of the division's all-time scoring list with 260 and Kane says he is inspired by the former Newcastle man's record.
"It's a lot of goals and I'm still a long way off but Shearer was an idol of mine growing up, to see how many goals he scored was incredible," Kane said.
"I take it season by season
I don't like looking too far ahead because you never know what can happen.
"But is it good to aim for? Definitely, they're the goals you dream of.
"When you're a younger player, you watch them scoring goals week in and week out, so to be doing that now is a dream come true."
Kane's 21 goals this season means he moves two clear of Jamie Vardy and three ahead of Romelu Lukaku in the race for the Golden Boot.
If the 22-year-old can hold off his scoring rivals, he would become the first Englishman to finish top of the charts since Kevin Phillips hit 30 for Sunderland in 1999-2000.
As England prepare to face Germany and Holland over the upcoming international break, Kane hopes his excellent form will help other young English forwards make the step up at the highest level.
"If I can be a role model or if I can maybe make another manager play a young player coming through, rather than buy a player, that's incredible," Kane said.
"I think sometimes managers like to buy players because they're more experienced from abroad or when they've got players under their nose that will give everything to the club they've been brought up with.
"The more people get chances at a young age, I think you'll see more talent coming through as we have done this season."
Tottenham's comfortable win over Bournemouth reduced the gap behind Leicester back to five points while Eddie Howe's side remain 13th, 12 points above the relegation zone.
Kane's opener came after just 44 seconds and the visitors never recovered as the Spurs forward made it two soon after before Christian Eriksen added a third in the second half.
Bournemouth defender Steve Cook said: "Conceding a goal after 44 seconds against a top-class team meant our game plan went out the window.
"It set the tone for the whole game
It was a massive kick in the teeth
In the second half we got a bit of respect back but they were excellent.
"That's where we want to be, what we want to be like
It shows the gap
We're up for the challenge
Tottenham I thought were unplayable today."
Bournemouth are all-but guaranteed safety, having accumulated 38 points with seven games left, but Cook insists there is no room for complacency.
"Everyone is very disappointed, there were some very strong words," Cook added.
"We won't be taking our foot off the gas
No-one is happy
We still have a points mark to get to, the magic 40, and we're still not there
There is work to do."
Source : PA
Source: PA